Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T13:15:16.202Z Has data issue: false hasContentIssue false

Critical branching processes

Published online by Cambridge University Press:  01 July 2016

Peter Ney*
Affiliation:
University of Wisconsin, Madison

Abstract

This paper develops a comparison method for critical branching processes. The method is applied to prove the exponential limit law for the multi-type age-dependent process under second moment conditions.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1974 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Athreya, K. and Ney, P. (1972) Branching Processes. Springer-Verlag, Heidelberg.CrossRefGoogle Scholar
Chover, J. and Ney, P. (1968) The non-linear renewal equation. J. Analyse Math. 21, 381413.CrossRefGoogle Scholar
Goldstein, M. (1969) Critical age-dependent branching processes. , University of Wisconsin.Google Scholar
Goldstein, M. (1971) Critical age-dependent branching processes. Z. Wahrscheinlichkeitsth. 17, 7488.CrossRefGoogle Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer, Berlin.CrossRefGoogle Scholar
Heathcote, C. R. and Seneta, E. (1966) Inequalities for branching processes. J. Appl. Prob. 3, 261267.CrossRefGoogle Scholar
Joffe, A. and Spitzer, F. (1967) On multitype branching processes with p ≦ 1. J. Math. Anal. Appl. 19, 409430.CrossRefGoogle Scholar
Seneta, E. (1967) On the transient behavior of a Poisson branching process. J. Austral. Math. Soc. 7, 465480.CrossRefGoogle Scholar
Seneta, E. (1968) Asymptotic properties of subcritical branching processes. J. Austral. Math. Soc. 8, 671682.CrossRefGoogle Scholar
Weiner, H.J. (1965) Asymptotic properties of an age-dependent branching process. Ann. Math. Statist. 36, 15651568.CrossRefGoogle Scholar
Weiner, H.J. (1970) On multitype critical age-dependent branching processes. J. Appl. Prob. 7, 523543.CrossRefGoogle Scholar